S-boxes play a central role in the design of symmetric cipher schemes.For stream cipher appli-cations,an s-box should satisfy several criteria such as high nonlinearity,balanceness,correlation immunity,and so on.In th...S-boxes play a central role in the design of symmetric cipher schemes.For stream cipher appli-cations,an s-box should satisfy several criteria such as high nonlinearity,balanceness,correlation immunity,and so on.In this paper,by using disjoint linear codes,a class of s-boxes possessing high nonlinearity and 1st-order correlation immunity is given.It is shown that the constructed correlation immune S-boxes can possess currently best known nonlinearity,which is confirmed by the example 1st-order correlation immune(12,3)s-box with nonlinearity 2000.In addition,two other frameworks concerning the criteria of balanced and resiliency are obtained respectively.展开更多
The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this ...The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.展开更多
Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanc...Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanche criterion （SAC） is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction technique, two new methods to construct cheating immune secret sharing functions are proposed.展开更多
In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to...In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.展开更多
Cheating immune secret sharing in the unconditionally secure case are investigated in this paper.Constructionsof defining functions of cheating immune secret sharing on V_n are given,where n is any integer greater tha...Cheating immune secret sharing in the unconditionally secure case are investigated in this paper.Constructionsof defining functions of cheating immune secret sharing on V_n are given,where n is any integer greater than 5.Further-more,the obtained defining functions have good cryptographic properties.The nonlinearity of them is 2^(n-1)-2^(n/2+1) whenn≡0(mod 4)and 2^(n-1)-2^((?)n/2」+2) otherwise.And thedegree is「n/4(?).展开更多
This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic im...This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.展开更多
基金supported by the National Natural Science Foundation of China(62272360,61972303)Natural Science Basic Research Plan in Shaanxi Province of China(2023-JC-YB-570)the Key Research and Development Program of Shaanxi Province(2021GY-040).
文摘S-boxes play a central role in the design of symmetric cipher schemes.For stream cipher appli-cations,an s-box should satisfy several criteria such as high nonlinearity,balanceness,correlation immunity,and so on.In this paper,by using disjoint linear codes,a class of s-boxes possessing high nonlinearity and 1st-order correlation immunity is given.It is shown that the constructed correlation immune S-boxes can possess currently best known nonlinearity,which is confirmed by the example 1st-order correlation immune(12,3)s-box with nonlinearity 2000.In addition,two other frameworks concerning the criteria of balanced and resiliency are obtained respectively.
文摘The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.
基金Supported by the National Nature Science Foundation of China（ No. 60773003,60970120）.
文摘Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanche criterion （SAC） is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction technique, two new methods to construct cheating immune secret sharing functions are proposed.
基金the National Natural Science Foundation of China (Grant No. 60673081)the "863" project (Grant No. 2006AA01Z417)
文摘In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.
文摘Cheating immune secret sharing in the unconditionally secure case are investigated in this paper.Constructionsof defining functions of cheating immune secret sharing on V_n are given,where n is any integer greater than 5.Further-more,the obtained defining functions have good cryptographic properties.The nonlinearity of them is 2^(n-1)-2^(n/2+1) whenn≡0(mod 4)and 2^(n-1)-2^((?)n/2」+2) otherwise.And thedegree is「n/4(?).
基金supported by the National Key Basic Research Program of China under Grant No.2013CB834203the National Natural Science Foundation of China under Grant Nos.61472417 and 61472120the Research Council of Norway
文摘This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.
